NT
1
K
Khách
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VK
0
NT
3
B
16 tháng 11 2018
a, \(x^3-x^2-4\)
\(=x^3-2x^2+x^2-2x+2x-4\)
\(=x^2\left(x-2\right)+x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+x+2\right)\)
16 tháng 11 2018
a) \(x^3-x^2-4\)
\(=x^3-2x^2+x^2-2x+2x-4\)
\(=x^2\left(x-2\right)+x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+x+2\right)\)
b) \(x^8-98x^4+1\)
\(=\left(x^4\right)^2+2\cdot x^4\cdot1+1^2-100x^4\)
\(=\left(x^4+1\right)^2-\left(10x^2\right)^2\)
\(=\left(x^4-10x^2+1\right)\left(x^4+10x^2+1\right)\)
2 tháng 9 2017
b) x7 + x2 + 1 = (x7 – x) + (x2 + x + 1)
= x.(x6 – 1) + (x2 + x +1)
= x.(x3 - 1).(x3 +1) + (x2 + x +1)
= x.(x-1).(x2 + x +1).(x3 +1) + (x2 + x +1)
= (x2 + x +1).[x.(x-1).(x3 +1) + 1]
= (x2 + x +1).[(x2-x).(x3 +1) + 1]
= (x2 + x +1).(x5-x4 + x2 -x + 1
2 tháng 9 2017
\(h\left(x\right)=x^7+x^5+1=x^7+x^6+x^5-x^6+1=x^5\left(x^2+x+1\right)-\left(x^3+1\right)\left(x^3-1\right)\)
\(=x^5\left(x^2+x+1\right)-\left(x^3+1\right)\left(x-1\right)\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^5-x^4+x^3-x+1\right)\)
TN
16 tháng 6 2017
a)\(3x^2-8x+4\)
\(=3x^2-2x-6x+4\)
\(=x\left(3x-2\right)-2\left(3x-2\right)\)
\(=\left(x-2\right)\left(3x-2\right)\)
b)\(4x^4+81\)
\(=4x^4+36x^2+81-36x^2\)
\(=\left(2x^2+9\right)^2-36x^2\)
\(=\left(2x^2-6x+9\right)\left(2x^2+6x+9\right)\)
c)\(x^8+98x^4+1\)
\(=\left(x^8+2x^4+1\right)+96x^4\)
\(=\left(x^4+1\right)^2+16x^2\left(x^4+1\right)+64x^4-16x^2\left(x^4+1\right)+32x^4\)
\(=\left(x^4+8x^2+1\right)^2-16x^2\left(x^4-2x^2+1\right)\)
\(=\left(x^4+8x^2+1\right)^2-16x^2\left(x^4-2x^2+1\right)\)
\(=\left(x^4+8x^2+1\right)^2-\left(4x^3-4x\right)^2\)
\(=\left(x^4+4x^3+8x^2-4x+1\right)\left(x^4-4x^3+8x^2+4x+1\right)\)
d)\(x^4+6x^3+7x^2-6x+1\)
\(=x^4+3x^3-x^2+3x^3+9x^2-3x-x^2-3x+1\)
\(=x^2\left(x^2+3x-1\right)+3x\left(x^2+3x-1\right)-\left(x^2+3x-1\right)\)
\(=\left(x^2+3x-1\right)\left(x^2+3x-1\right)\)\(=\left(x^2+3x-1\right)^2\)
MT
3
25 tháng 5 2015
a) x8 + x + 1 = (x^2+x+1)*(x^6-x^5+x^3-x^2+1)
b) x^8 + 3x^4 + 4 = (x^4-x^2+2)*(x^4+x^2+2)
TN
2
HS
0
KN
3 tháng 7 2019
\(x^8+3x^4+4\)
\(=\left(x^8-x^6+2x^4\right)+\left(x^6-x^4+2x^2\right)+\left(2x^4-2x^2+4\right)\)
\(=x^4\left(x^4-x^2+2\right)+x^2\left(x^4-x^2+2\right)+2\left(x^4-x^2+2\right)\)
\(=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)
KN
3 tháng 7 2019
\(4x^4+4x^3+5x^2+2x+1\)
\(=\left(4x^4+2x^3+2x^2\right)+\left(2x^3+x^2+x\right)+\left(2x^2+x+1\right)\)
\(=2x^2\left(2x^2+x+1\right)+x\left(2x^2+x+1\right)+\left(2x^2+x+1\right)\)
\(=\left(2x^2+x+1\right)^2\)
KT
2 tháng 11 2018
\(x^8+x+1\)
\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)
\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)
MY
1
26 tháng 2 2015
x8 + x4 +1 = ( x8 + x7 + x6) - ( x7 + x6 + x5 ) + ( x5 + x4 + x3 ) - (x3 - x2 - x ) + ( x2 + x + 1)
= x6( x2 + x + 1 ) - x5( x2 + x + 1 ) + x3( x2 + x +1 ) - x( x2 + x +1 ) + ( x2 + x +1 )
= ( x2 + x +1 )( x6 - x5 + x3 - x + 1 )
x8 + 98x4 + 1
= (x8 + 2x4 + 1 ) + 96x4
= (x4 + 1)2 + 16x2(x4 + 1) + 64x4 - 16x2(x4 + 1) + 32x4
= (x4 + 1 + 8x2)2 – 16x2(x4 + 1 – 2x2) = (x4 + 8x2 + 1)2 - 16x2(x2 – 1)2
= (x4 + 8x2 + 1)2 - (4x3 – 4x)2
= (x4 + 4x3 + 8x2 – 4x + 1)(x4 - 4x3 + 8x2 + 4x + 1)